In an air-filled rectangular waveguide, the cutoff frequency of a TE10 mode is 5 GHz, whereas that of TE01 mode is 12 GHz. Calculate
(a) The dimensions of the guide
(b) The cutoff frequencies of the next three higher TE modes
(c) The cutoff frequency for TE11 mode if the guide is filled with a lossless material having εr = 2.25 and μr = 1.